As a general principle, you can't sail upwind without a balanced rig, meaning roughly equai amounts of mainsail and jib. '
This statement is misleading. Most modern sloop-rigged boats will sail very well to windward with the genoa alone, including being relatively close-hauled. You don't necessarily need to have any
mainsail out. Once in the BVI I sailed past a 50' ketch with a professional crew and flying all sails beating to windward, in a Pearson 10M with the genoa alone
While you can reach OK with just the main, most boats will do better (sail faster) with just a genoa. And, as you've noted, it's much easier to roll in or out to set the area needed for the wind conditions and point of sail.
When going upwind, most boats will go very slowly
under main alone. They really need a headsail in order to make the main an efficient contributor to boat speed. The difference is really dramatic
. Try it yourself: set a course closehauled in a decent wind, note your boatspeed, then drop (or furl) the headsail, leaving the full main. Your boatspeed will fall off to almost nothing. By the way, this isn't a bad way to sail up to a mooring in a strong wind.
Bottom line: for your trip I'd start out with just the genoa and see how it works. If the wind falls light and you need more sail area, then put up some main. Of course, an alternate strategy would be to tuck in a reef in the main before setting out, and unroll enough genoa to get your boatspeed up.